Systems of Linear/Quadratic Equations and Inequalities

Front

What is a system of linear equations?

Back

A set of two or more linear equations with the same variables.

Front

What does it mean if a system of equations has one solution?

Back

The lines intersect at exactly one point.

Front

What does it mean if a system of equations has no solutions?

Back

The lines are parallel and never intersect.

Front

What does it mean if a system of equations has infinitely many solutions?

Back

The lines coincide, meaning they are the same line.

Front

How do you determine the number of solutions in a system of linear equations?

Back

By analyzing the slopes and y-intercepts of the lines.

Front

What is a quadratic equation?

Back

An equation of the form ax² + bx + c = 0, where a, b, and c are constants.

Front

What is the vertex of a parabola?

Back

The highest or lowest point of the parabola, depending on its orientation.

Front

How do you find the vertex of a quadratic function?

Back

Using the formula x = -b/(2a) to find the x-coordinate, then substituting back to find the y-coordinate.

Front

What is the discriminant in a quadratic equation?

Back

The value of b² - 4ac, which determines the nature of the roots.

Front

What does a positive discriminant indicate?

Back

Two distinct real solutions.